def p_ge

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/rconst.bend:51

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as FO

51# 2^255 <= p
52def p_ge(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(C.shift(255n, one), 1n+K.pp(one)) == True{} : Bool}:
53  +pp = K.pp(one)
54  +c = FS.cp(one)
55  +e1 = Equal.trans(Nat, Nat.add(1n+pp, c), C.shift(256n, one), Nat.add(C.shift(255n, one), C.shift(255n, one)), K.hm_p(one, h1), Equal.sym(Nat, Nat.add(C.shift(255n, one), C.shift(255n, one)), C.shift(256n, one), K.shift_twice(255n, one)))
56  +ch = N.le_trans(c, C.shift(33n, one), C.shift(255n, one), K.cp_le(one, h1), K.shift_le_k(33n, 255n, one, 222n, {==}))
57  FO.lt_p_half(C.shift(255n, one), 1n+pp, c, e1, ch)